The angle criterion
type: Item
instance of: scholarly article
title: The angle criterion
zbMATH Open document ID: 0662.49018
DOI: 10.1007/BF01393905
published in: Inventiones Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143660
review text: In 1983 Frank Morgan conjectured an ``angle criterion'': a pair of oriented m-planes in \(R^ n\) is area-minimizing if and only if the characterizing angles between them satisfy the inequality \(\beta_ m\leq \beta_ 1+...+\beta_{m-1}.\) \textit{F. Morgan} [Math. Ann. 261, 101-110 (1982; Zbl 0549.49029)] proved the conjecture for \(m=2\). Further results were obtained for \(m=3\) and \(m=4\) by \textit{J. Dadok} and \textit{R. Harvey} [Duke Math. J. 50, 1231-1243 (1983; Zbl 0535.49030)] and \textit{J. Dadok}, \textit{R. Harvey} and \textit{F. Morgan} [Trans. Am. Math. Soc. 307, No.1, 1-40 (1988)] and for \(m=5\) by M. Messaoudene (unpublished). \textit{D. Nance} [Math. Ann. 279, 161-164 (1987)] proved that for all m, any pair of m-planes satisfying the criterion is area-minimizing. This paper completes the proof of the angle conjecture in all dimensions, by providing surfaces of less area for pairs not satisfying the condition.
Mathematics Subject Classification ID: 49Q15
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 4082383
zbMATH Keywords: area-minimizing surface
zbMATH Keywords: angle criterion
author: Gary R. Lawlor
reviewed by: Constantin Udrişte
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4082383